The orbit of a spacecraft about the sun has a perihelion distance of 0.5 AU and an aphelion of 3.5 AU.? What is the spacecraft’s orbital period?

1 Answer
Phillip E.
Jan 18, 2016

The period would be about 2.828 years.

Explanation:

The perihelion distance is #d_p=a(1-e)# and the aphelion distance is #d_a=a(1+e)#. Where #a# is the semi-major axis and #e#is the eccentricity of the orbit.

Adding the two equations gives #2a=d_p+d_a#. So the semi-major axis of the space craft is #2a=0.5+3.5#. Hence #a=2#AU.

Kepler's third law relates the semi-major axis to the orbital period #T^2=a^3#. For the spacecraft #T^2=8#. This gives an orbital period #T=2.828# years.

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